Instead of Rechamberring a classic old rifle with a very good chance of it not shooting any better I would look into a Rem take off barrel in 223 (all 700, Model 7 and 600/660 fit) and have it fitted. That way you can always put the old barrel on or sell it as an original . I did that with my 722 300Savage, I put a 22-250 barrel from a Rem LVSF on it. If you do this be sure you tell the smith that you want to be able to return it to original.
AWS